Annular gear machines (gerotor machines) possess an inner ring and an outer ring, each of them provided with teeth and tooth gaps regularly distributed about the circumference. The rotational axes of the inner ring and the outer ring are eccentrically set off from each other. The inner ring usually has exactly one tooth less than there are tooth gaps provided at the inner toothing of the outer ring. Annular gear machines today are often used as annular gear pumps, for example, in vehicles as the main pump of the internal combustion engine. The displacement space formed by tooth gaps and housing walls changes with the rotation of the annular gears, so that delivery of hydraulic fluid is accomplished. The delivery volume per revolution is constant in this case. The teeth of the outside-toothed inner ring are usually formed according to various rules for the roll-off behavior of the outer ring. One such known rule is, for example, the movement of the generating contour according to the laws of cycloidal curves rolling on a fixed pitch circle.
The geometries chosen have substantial influence on the delivery behavior, the efficiency, the quiet running and the wear of an annular gear machine. In particular, the design process can configure the tooth shapes, the eccentricity of the rotational axes of the two annular gears, and the remaining play between individual tooth segments without a direct dependency on the external conditions that are dictated by the attached drive unit.
Tooth profiles for annular gears are known from U.S. Pat. No. 3,709,055 that have circular tooth tips and circular tooth base profiles that are joined to each other via straight flanks. There is also a method known from this patent for generating such tooth shapes that can be used, for example in annular gear machines. With the method proposed there, however, it is not possible to achieve a major goal of an annular gear machine, namely, to configure a geometrically closed delivery cell at all times between the two annular gears in the course of the motion, or if so only in very narrow limits. This is especially important to the efficiency of the annular gear pump and the pressures which can be achieved.
U.S. Pat. No. 2,960,884 likewise describes annular gear machines and ways of determining the tooth geometry. The tooth generating method indicated there is mainly suited to accomplishing an evolvent type motion sequence between functionally coupled tooth geometries. The aforementioned main goal of an annular gear machine, namely, uniform tightness of the delivery cell over the entire angle of rotation in the motion sequence, can only be partly accomplished with this method.
JP 10-205458 A indicates a method for determining the tooth geometry of an annular gear pump. Here, the tooth of an outer ring is described by coupled circular arcs, after which the toothing of the inner ring can be generated. The definition of special geometries of toothing schemes with undercuts or to reduce the Hertzian pressure is hardly possible, if at all, due to being limited to describing the tooth shape by means of a defined number of circular arcs.
From EP 1 340 913 B1 and DE 102 08 408 A1 there is known a gear machine that has uses as an annular gear pump. The primary goal here is to optimize the geometry of the gears in order to lessen the noise during operation of the pump. The tooth tips and tooth roots used have a geometry that is described by curves of second or higher order, while the tooth roots or the flanks of the tooth roots are formed by circular arcs. To determine the profile contours of the toothing it is proposed to specify the inner toothing of the outer rotor as the master toothing. The tooth root profile contour of the inner rotor is derived kinematically from the tooth tip profile contour of the inner toothing by the law of gear meshing, while the tooth tip profile contour is obtained from the generating cuts of the tooth root profile contour of the inner toothing. The bearing points of the polygons representing the tooth roots of the outer toothing are determined by the law of gear meshing, while the bearing points of the spline functions representing the tooth tips of the outer toothing are found by a generating cut method. However, studies have shown that the tooth shapes which can be generated in this way lead to limitations in regard to efficiency and flow conditions in the annular gear machine. Another drawback is the rigid definition of the root fillet, which has limiting effect on the configuration of a dirt catching space, for example.
U.S. Pat. No. 5,030,072 reveals a method for the design of the tooth shape of an annular gear machine, wherein at first a radial cam distance is determined and then a cam radius is varied by iteration until a single-point distance and a double-point distance equal the determined cam distance.
DE 30 26 222 A1 shows an annular gear pump in which the theoretical tooth shape of the pinion is determined by rolling off the pinion pitch circle on the hollow wheel pitch circle. One starts with a particular shape of toothing for the design of the tooth shape of the pinion. The method is only applicable to this particular tooth shape.
U.S. Pat. No. 2,666,336 shows a method for the design of toothings for rotoids which have different tooth relations, unlike gerotors (annular gear machines). The starting point is an outer circle with diameter A and a pinion circle with diameter B, from which one gets the eccentricity E.
In the article “Design of deviatation-function based gerotors”, Shih-Hsi Tong et al., Mechanism and Machine Theory 44 (2009) 1595-1606, a novel method is discussed for the generating of gerotor profiles. This method is based on the use of variance functions, but it requires time-consuming calculations and design steps and can lead to dimensioning problems, especially when undercuts are present.
One problem of the present invention is, starting from the prior art, to indicate a method for the generating of the tooth shapes of inner and outer ring of an annular gear machine, especially an annular gear pump, which is easy to implement, requires no extensive knowledge of mathematical relations, and affords the designer a broad dimensioning freedom to satisfy different demands on the annular gear machine being created. The goal is to dispense with the heretofore customary description of the tooth contours by cycloids, ellipses, evolvents, circular arcs, or similar mathematically easily described curve segments, since these limit the possible geometries of the tooth shapes. At the same time, the tooth shapes generated should be described with sufficient accuracy by the currently available technical aids, especially CAD and CAM systems, so as to enable an automated manufacturing of corresponding inner and outer rings with available machine tools.
The above problem is solved by a method according to the enclosed claim 1.